关于计时事件图的同步性

计时事件图可用于通信、制造等系统的建模、分析、控制和优化.运用极大加代数方法研究计时事件图的同步性.对自治系统,在极大子系统之间添加时间限制来得到系统的同步,并给出同步系统的一些性质和系统同步的最短周期时间.对非自治系统,通过因果反馈得到系统的同步性,并给出较短的周期时间.     

与环境相关的非线性投资发展系统解的性质

研究了与环境相关的非线性投资发展系统,该系统为含有非线性和非局部边界条件的分布参数系统.运用泛函分析和积分方程的理论,证明了系统解的性质.其结果可为实际问题的研究提供理论基础.     

力觉临场感遥操作机器人系统的鲁棒控制

力觉临场感遥操作机器人系统的通信通道中存在通信时延,而且在机器人和环境建模中,系统参数存在不确定性,以致可能造成系统不稳定和操作性能降低.针对通信时延和系统不确定性,建立系统的状态方程,利用鲁棒控制理论,提出用力、位置和速度反馈的控制方法.分析与实验表明,用该方法设计的控制器能使系统鲁棒渐近稳定,而且能使系统完全透明.     

广义同步化流形的Holder连续性

证明了两个不同的混沌系统线性耦合时能实现广义同步化,在一定条件下广义同步化流形是Holder连续的.采用的思想是Temam的无穷维动力系统的惯性流形理论的改进.在线性耦合下两个混沌系统具有吸收集和吸引子的基础上,通过定义在一个函数类上的映射满足Schauder不动点定理,从而得到广义同步化流形,该广义同步化流形具有不变性.又证明了存在分数维的指数吸引子,指数吸引子与广义同步流形的交集具有指数吸引性.数值仿真证实了理论的正确性.在驱动系统和响应系统外引入辅助系统,辅助系统与响应系统的完全同步化表明了驱动系统和响应系统的广义同步化.     

一类非线性微分代数系统的零动态

控制系统的零动态是系统一种内部动态品质,其行为与系统的许多性质相联系,如系统的稳定性,反馈镇定与输出跟踪等.针对一类非线性微分代数系统,提出了输出零子流形和零动态的概念.利用M-导数方法,探讨了此类系统的输出零子流形的性质,并给出了此类系统的输出零子流形和零动态算法,也讨论了该算法的一些性质.最后,给出一个例子说明如何利用系统的零动态来讨论系统的反馈稳定化问题.     

复杂系统的一般数学框架(Ⅰ)

复杂系统的基本和最简单的结构就是网络.根据这一思想,本系列论文拟发展一套处理复杂系统的新数学框架.本文详细论述了系统的概念、一般描述方法:系统=(硬部,软部,环境)和局整关系,包括子系统、元素与系统的关系和系统与系统的关系;给出了系统运算的基本法则;简要论述了系统的软、硬部之间的诱导转化.     

基于观测器的模糊时滞系统的指数稳定控制

研究一类模糊时滞系统的指数稳定和基于观测器的模糊控制问题.在系统状态未知的情况下,通过设计系统的模糊观测器利用矩阵不等式分析的方法给出了系统指数稳定条件和基于观测器的动态输出反馈控制器设计方案.仿真结果说明了所提方法的有效性.     

平面不可压缩Navier-Stokes方程五模系统的力学机理及能量演化

该文研究了平面不可压缩Navier-Stokes方程五模系统的力学机理及能量演化问题,通过将五模混沌系统转换成Kolmogorov形系统,把系统的力矩分为三种类型:惯性力矩,耗散力矩和外力矩.通过不同力矩的结合分析和研究了系统产生混沌的关键因素和物理意义.讨论了能量与雷诺数之间的关系.研究表明三种力矩的耦合是产生混沌的必要条件,而且只有耗散力矩和驱动力矩(外力矩)相匹配时,系统才能产生混沌,其中任何两种力矩耦合均不可能产生混沌.外力矩给系统提供能量,导致系统失稳出现分岔与混沌.引进Casimir函数分析系统的动力学行为和能量演化,并估计混沌吸引子的界.Casimir函数反映了能量转换和轨道与平衡点间的距离.     

具有内阻尼和边界反馈控制的一类Euler-Bernoulli梁方程的Riesz基性质

考虑一类具有内阻尼和边界反馈控制的一维Euler-Bernoulli梁方程.中导出系统特征值和特征函数的渐近表达式,并且通过Riesz基生成定理的优点,证明该系统是一个Riesz系统,即该系统存在一列广义特征函数构成能量状态空间的一组Riesz基.从而,系统的谱决定增长条件成立,进而证明系统的指数稳定性.     

广义同步化流形的Hlder连续性

证明了两个不同的混沌系统线性耦合时能实现广义同步化,在一定条件下广义同步化流形是Hlder连续的.采用的思想是Temam的无穷维动力系统的惯性流形理论的改进.在线性耦合下两个混沌系统具有吸收集和吸引子的基础上,通过定义在一个函数类上的映射满足Schauder不动点定理,从而得到广义同步化流形,该广义同步化流形具有不变性.又证明了存在分数维的指数吸引子,指数吸引子与广义同步流形的交集具有指数吸引性.数值仿真证实了理论的正确性.在驱动系统和响应系统外引入辅助系统,辅助系统与响应系统的完全同步化表明了驱动系统和响应系统的广义同步化.     

Linear birth and death models and associated Laguerre and Meixner polynomials

We study birth and death processes with linear rates λ_n = n + α + c + 1, μ_{n + 1} = n + c, n 0 and μ₀ is either zero or c. The spectral measures of both processes are found using generating functions and the integral transforms of Laplace and Stieltjes. The corresponding orthogonal polynomials generalize Laguerre polynomials and the choice μ₀ = c generates the associated Laguerre polynomials of Askey and Wimp. We investigate the orthogonal polynomials in both cases and give alternate proofs of some of the results of Askey and Wimp on the associated Laguerre polynomials. We also identify the spectra of the associated Charlier and Meixner polynomials as zeros of certain transcendental equations.     

Distributive and Multiplication Modules and Rings

We study rings in which every ideal is a finitely generated multiplication right ideal.     

Affine-inscribed and affine-circumscribed polygons and polytopes

Five theorems on polygons and polytopes inscribed in (or circumscribed about) a convex compact set in the plane or space are proved by topological methods. In particular, it is proved that for every interior point O of a convex compact set in ℝ³, there exists a two-dimensional section through O circumscribed about an affine image of a regular octagon. It is also proved that every compact convex set in ℝ³ (except the cases listed below) is circumscribed about an affine image of a cube-octahedron (the convex hull of the midpoints of the edges of a cube). Possible exceptions are provided by the bodies containing a parallelogram P and contained in a cylinder with directrix P. Bibliography: 29 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 286–298. Translated by B. M. Bekker.     

Partitions and pairwise sums and products

A seven cell partition of N is constructed with the property that no infinite set has all of its pairwise sums and products in any one cell. A related Ramsey Theory question is shown to have different answers for two and three cell partitions.     

Ritz and harmonic Ritz values and the convergence of FOM and GMRES

The Ritz and harmonic Ritz values are approximate eigenvalues, which can be computed cheaply within the FOM and GMRES Krylov subspace iterative methods for solving non‐symmetric linear systems. They are also the zeros of the residual polynomials of FOM and GMRES, respectively. In this paper we show that the Walker–Zhou interpretation of GMRES enables us to formulate the relation between the harmonic Ritz values and GMRES in the same way as the relation between the Ritz values and FOM. We present an upper bound for the norm of the difference between the matrices from which the Ritz and harmonic Ritz values are computed. The differences between the Ritz and harmonic Ritz values enable us to describe the breakdown of FOM and stagnation of GMRES. Copyright © 1999 John Wiley & Sons, Ltd.     

Beliefs and beyond: affect and the teaching and learning of mathematics

The importance of beliefs for the teaching and learning of mathematics is widely recognized among mathematics educators. In this special issue, we explicitly address what we call “beliefs and beyond” to indicate the larger field surrounding beliefs in mathematics education. This is done to broaden the discussion to related concepts (which may not originate in mathematics education) and to consider the interconnectedness of concepts. In particular, we present some new developments at the conceptual level, address different approaches to investigate beliefs, highlight the role of student beliefs in problem-solving activities, and discuss teacher beliefs and their significance for professional development. One specific intention is to consider expertise from colleagues in the fields of educational research and psychology, side by side with perspectives provided by researchers from mathematics education.